Ok, I've been using solidworks for almost 8 years now. And they haven't fixed item selection yet, so I have to keep asking this question that everyone asks.

I have a big assembly and a lot of items in many different subassemblies.

I select items in the view, but I cannot export them simply by going to save-as or doing an isolate/save-as

I have to do an invert selection, and then do a save-as. Fine.

But when I select items in the view, I cannot do an invert selection in view, I HAVE to do it in model tree. But my items don't automatically select themselves in Model Tree, so I don't know where they are. And I HAVE to click on the selected item in the model tree, I can't just do a right click in the model tree.

So I'm stuck having to look for these parts in the model tree out of hundreds of parts.

Not sure whether this will help. You can try selecting the parts that you do not want and save selection set. This will appear in the assembly tree where you can expand the selection set. From there, you should be able to select all and right click to invert selection.